Consider a $1-$bit full adder. There are three inputs A$,$ B and Cin $($carry$-$in$)$ and two outputs S $($sum$)$ and

Cout $($carry$-$out$).$ The Boolean expressions for the two outputs are:

S $=$ A $$ B $$ Cin

Cout $=$ AB $+$ ACin $+$ BCin

Implement these two functions using Multiplexer $($MUX$)$ logic. Consider two cases:

a$)$ Use $8$:$1$ Mux

b$)$ Use not gates and $4$:$1$ Mux